Sr Examen
Lógica matemática/ CBA+D¬C¬B¬A

Expresión CBA+D¬C¬B¬A

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

    Ha introducido [src] 
    (a∧b∧c)∨(d∧(¬a)∧(¬b)∧(¬c))
    $$\left(a \wedge b \wedge c\right) \vee \left(d \wedge \neg a \wedge \neg b \wedge \neg c\right)$$
    Solución detallada
    $$\left(a \wedge b \wedge c\right) \vee \left(d \wedge \neg a \wedge \neg b \wedge \neg c\right) = \left(a \vee \neg b\right) \wedge \left(a \vee \neg c\right) \wedge \left(b \vee \neg a\right) \wedge \left(b \vee \neg c\right) \wedge \left(c \vee d\right) \wedge \left(c \vee \neg a\right) \wedge \left(c \vee \neg b\right)$$
    Simplificación [src]
    $$\left(a \vee \neg b\right) \wedge \left(a \vee \neg c\right) \wedge \left(b \vee \neg a\right) \wedge \left(b \vee \neg c\right) \wedge \left(c \vee d\right) \wedge \left(c \vee \neg a\right) \wedge \left(c \vee \neg b\right)$$ 
    (c∨d)∧(a∨(¬b))∧(a∨(¬c))∧(b∨(¬a))∧(b∨(¬c))∧(c∨(¬a))∧(c∨(¬b))
    Tabla de verdad 
    +---+---+---+---+--------+
| a | b | c | d | result |
+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+
    FNDP [src]
    $$\left(a \wedge b \wedge c\right) \vee \left(d \wedge \neg a \wedge \neg b \wedge \neg c\right)$$ 
    (a∧b∧c)∨(d∧(¬a)∧(¬b)∧(¬c))
    FND [src]
    $$\left(a \wedge b \wedge c\right) \vee \left(a \wedge b \wedge c \wedge d\right) \vee \left(a \wedge b \wedge c \wedge \neg a\right) \vee \left(a \wedge b \wedge c \wedge \neg b\right) \vee \left(a \wedge b \wedge c \wedge \neg c\right) \vee \left(a \wedge c \wedge \neg a \wedge \neg c\right) \vee \left(b \wedge c \wedge \neg b \wedge \neg c\right) \vee \left(c \wedge \neg a \wedge \neg b \wedge \neg c\right) \vee \left(d \wedge \neg a \wedge \neg b \wedge \neg c\right) \vee \left(a \wedge b \wedge c \wedge d \wedge \neg a\right) \vee \left(a \wedge b \wedge c \wedge d \wedge \neg b\right) \vee \left(a \wedge b \wedge c \wedge d \wedge \neg c\right) \vee \left(a \wedge b \wedge c \wedge \neg a \wedge \neg b\right) \vee \left(a \wedge b \wedge c \wedge \neg a \wedge \neg c\right) \vee \left(a \wedge b \wedge c \wedge \neg b \wedge \neg c\right) \vee \left(a \wedge b \wedge d \wedge \neg a \wedge \neg b\right) \vee \left(a \wedge c \wedge d \wedge \neg a \wedge \neg c\right) \vee \left(a \wedge c \wedge \neg a \wedge \neg b \wedge \neg c\right) \vee \left(a \wedge d \wedge \neg a \wedge \neg b \wedge \neg c\right) \vee \left(b \wedge c \wedge d \wedge \neg b \wedge \neg c\right) \vee \left(b \wedge c \wedge \neg a \wedge \neg b \wedge \neg c\right) \vee \left(b \wedge d \wedge \neg a \wedge \neg b \wedge \neg c\right) \vee \left(c \wedge d \wedge \neg a \wedge \neg b \wedge \neg c\right) \vee \left(a \wedge b \wedge c \wedge d \wedge \neg a \wedge \neg b\right) \vee \left(a \wedge b \wedge c \wedge d \wedge \neg a \wedge \neg c\right) \vee \left(a \wedge b \wedge c \wedge d \wedge \neg b \wedge \neg c\right) \vee \left(a \wedge b \wedge c \wedge \neg a \wedge \neg b \wedge \neg c\right) \vee \left(a \wedge b \wedge d \wedge \neg a \wedge \neg b \wedge \neg c\right) \vee \left(a \wedge c \wedge d \wedge \neg a \wedge \neg b \wedge \neg c\right) \vee \left(b \wedge c \wedge d \wedge \neg a \wedge \neg b \wedge \neg c\right) \vee \left(a \wedge b \wedge c \wedge d \wedge \neg a \wedge \neg b \wedge \neg c\right)$$ 
    (a∧b∧c)∨(a∧b∧c∧d)∨(a∧b∧c∧(¬a))∨(a∧b∧c∧(¬b))∨(a∧b∧c∧(¬c))∨(a∧c∧(¬a)∧(¬c))∨(b∧c∧(¬b)∧(¬c))∨(a∧b∧c∧d∧(¬a))∨(a∧b∧c∧d∧(¬b))∨(a∧b∧c∧d∧(¬c))∨(c∧(¬a)∧(¬b)∧(¬c))∨(d∧(¬a)∧(¬b)∧(¬c))∨(a∧b∧c∧(¬a)∧(¬b))∨(a∧b∧c∧(¬a)∧(¬c))∨(a∧b∧c∧(¬b)∧(¬c))∨(a∧b∧d∧(¬a)∧(¬b))∨(a∧c∧d∧(¬a)∧(¬c))∨(b∧c∧d∧(¬b)∧(¬c))∨(a∧c∧(¬a)∧(¬b)∧(¬c))∨(a∧d∧(¬a)∧(¬b)∧(¬c))∨(b∧c∧(¬a)∧(¬b)∧(¬c))∨(b∧d∧(¬a)∧(¬b)∧(¬c))∨(c∧d∧(¬a)∧(¬b)∧(¬c))∨(a∧b∧c∧d∧(¬a)∧(¬b))∨(a∧b∧c∧d∧(¬a)∧(¬c))∨(a∧b∧c∧d∧(¬b)∧(¬c))∨(a∧b∧c∧(¬a)∧(¬b)∧(¬c))∨(a∧b∧d∧(¬a)∧(¬b)∧(¬c))∨(a∧c∧d∧(¬a)∧(¬b)∧(¬c))∨(b∧c∧d∧(¬a)∧(¬b)∧(¬c))∨(a∧b∧c∧d∧(¬a)∧(¬b)∧(¬c))
    FNCD [src]
    $$\left(a \vee d\right) \wedge \left(a \vee \neg b\right) \wedge \left(a \vee \neg c\right) \wedge \left(b \vee \neg a\right) \wedge \left(b \vee \neg c\right) \wedge \left(c \vee \neg a\right) \wedge \left(c \vee \neg b\right)$$ 
    (a∨d)∧(a∨(¬b))∧(a∨(¬c))∧(b∨(¬a))∧(b∨(¬c))∧(c∨(¬a))∧(c∨(¬b))
    FNC [src]
    Ya está reducido a FNC
    $$\left(a \vee \neg b\right) \wedge \left(a \vee \neg c\right) \wedge \left(b \vee \neg a\right) \wedge \left(b \vee \neg c\right) \wedge \left(c \vee d\right) \wedge \left(c \vee \neg a\right) \wedge \left(c \vee \neg b\right)$$ 
    (c∨d)∧(a∨(¬b))∧(a∨(¬c))∧(b∨(¬a))∧(b∨(¬c))∧(c∨(¬a))∧(c∨(¬b))
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